# Level I Quantitative Methods

## Frequency Distributions

A frequency distribution is nothing more nor less than a grouping of data into a number of intervals or “bins”.  It is most commonly presented as either a histogram or as a frequency polygon.  For example, if you were to capture and measure the heights (in meters) of 500 giraffes, you might produce a table […]

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## Basics of Statistics

There are a number of statistical terms defined in the Level I CFA curriculum, so I decided that it would be a good idea to consolidate them into one place: here. Descriptive Statistics vs. Inferential Statistics Descriptive statistics summarizes the characteristics of a data set.  For example, suppose that you acquire a sample of 500 […]

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## Money-Weighted Rate of Return (MWRR) vs. Time-Weighted Rate of Return (TWRR)

Suppose that you manage an investment portfolio to which cash is added periodically, and from which cash is removed periodically.  A reasonable question to ask is this: How should you determine the correct overall return on the portfolio over a period of time, the one that you should report to clients and prospective clients?  In […]

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## Net Present Value (NPV) and Internal Rate of Return (IRR)

Net present value (NPV) and internal rate of return are intimately related to each other, and each is designed to answer a simple question: should I shell out my hard earned to make a given investment?  The investment could be: Buying a bond Buying a stock Buying some machinery Buying a truck Buying a company […]

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## Annuities and Perpetuities

The word annuity traces its origins back to the Latin annuus: yearly.  Such is the name of payments that are paid annually, or on some other regular schedule; i.e., the payments are periodic.  The payments can be fixed (i.e., equal), increasing or decreasing at a specified rate, or irregular (essentially random).  They can made at […]

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## Interest Rate Basics

This article will cover the basics on interest rates: what they are, how to interpret them, how they’re measured, that sort of thing.  More complex ideas on interest rates appear in separate articles. At its most basic, interest is rent paid to use money.  Just as you might pay rent to use someone else’s house […]

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## Chi-Square (χ²) Distribution

First things first: it’s chi-square, not chi squared. There is a family of chi-square distributions: one for each degree of freedom k, k = 1, 2, 3, . . .  For a given value of k, the chi-square distribution with k degrees of freedom is the probability distribution of the sum of the squares of […]

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## Probability Distributions

In the Level I CFA curriculum there are, at the moment, these probability distributions that candidates must understand and be able to use: Discrete distributions Binomial Uniform  Continuous distributions Chi-square (χ2) F Lognormal Normal Student’s t Uniform This article will describe discrete and continuous distributions in general and how to use them; the links, above, […]

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## Continuous Uniform Distribution

Before reading this article, make sure that you have read the article on probability distributions in general. The continuous uniform distribution is almost as easy to understand as the discrete uniform distribution: although it has an infinite number of possible values that it can take – it is continuous, after all – those values comprise […]

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## Discrete Uniform Distribution

Before reading this article, make sure that you have read the article on probability distributions in general. The discrete uniform distribution is arguably one of the easiest to understand: it has only a finite number of possible values that it can take, and the probability of taking on any value is the same as the […]

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